The lines represent the inequalities
.
Further explanation:
The linear equation with slope m and intercept c is given as follows.

The formula for slope of line with points
and
can be expressed as,

Given:
The inequalities are as follows.
1.
2. 
3.
4. 
Explanation:
The blue line intersects y-axis at
, therefore the y-intercept is 4.
The blue line intersect the points that are
and
.
The slope of the line can be obtained as follows.

The slope of the line is m = 2.
Now check whether the inequality included origin or not.
Substitute
in equation 

0 is not greater than 4 which mean that the inequality doesn’t include origin.
Therefore, the blue line is y > 2x + 4.
Solve inequality ax-3y > 6 to obtain the standard form of inequality.

The y intercept of the equation is -2 and the y-intercept of the line is 2.
Therefore, the inequality doesn’t satisfy the line.
Solve inequality bx + 3y > 6 to obtain the standard form of inequality.

The y intercept of the equation is 2 and the y-intercept of the line is 2.
Therefore, the inequality bx + 3y > 6 satisfies the line.
Option 1 is not correct as it doesn’t satisfy the inequalities of the graph.
Option 2 is correct as the inequalities satisfy the graph.
Option 3 is not correct as the y-intercept is not 4.
Option 4 is not correct as the y-intercept is not 4.
Hence,
is correct
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear inequalities
Keywords: numbers, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.